A feeder of a distribution network typically consists of many different types of over-headline and/or cable sections. This means that electrically the feeder is non-homogeneous.
Conductor parameters (resistance, inductance and capacitance) can vary greatly, depending on conductor type and configuration. Especially overhead-line and cable parameters differ from each other. Typically, the angle of the positive sequence impedance on cables is substantially less than on overhead-lines. Also different overhead-line types differ from each other. The same applies to cables.
Inherently, the result of an impedance based fault localization algorithm is an electrical length to fault, i.e. the result is in the form of (loop) impedance. FIG. 1 illustrates a fault loop model for a phase-to-earth fault at point F of an electric line (feeder). For phase-to-earth faults, the fault loop impedance is:ZLoop=d·(Z1+ZN)+RF   (1)
Where
d=fault location in per unit value (0 . . . 1)
Z1=positive sequence impedance of the line=R1+j·X1 
R1=positive sequence resistance of the line
X1=positive sequence reactance of the line
ZN=earth return path impedance of the line=(Z0−Z1)/3=RN+j·XN 
RN=earth return path resistance of the line=(R0−R1)/3
XN=earth return path reactance of the line=(X0−X1)/3
Z0=zero sequence impedance of the line=R0+j·X0 
R0=zero sequence resistance of the line
X0=zero sequence reactance of the line
RF=fault resistance. For phase-to-earth loop this typically includes arc and tower footing resistances.
In the case of a non-homogeneous line, the impedances of individual line sections vary and the line impedance is the sum of the impedances of the sections:Z1=Z1A+Z1B+Z1C+ . . .ZN=ZNA+ZNB+ZNC+ . . .
where
Z1A=positive sequence impedance of line section A,
Z1B=positive sequence impedance of line section B,
Z1C=positive sequence impedance of line section C,
ZNA=earth return path impedance of line section A,
ZNB=earth return path impedance of line section B,
ZNC=earth return path impedance of line section C.
As a result, the electrical distance to fault (an ohmic value) cannot be directly converted into a physical distance, such as miles, kilometers or per unit value. However, while distribution lines are in most cases non-homogeneous, the impedance algorithms applied in protective relays typically do not take this into account, which may cause a considerable error in a fault location estimate.
Document U.S. Pat. No. 6,483,435 discloses a method and device for fault location for distribution networks. In the solution disclosed, the non-homogeneity of a feeder is taken into account. The solution, however, is computationally rather burdensome as e.g. individual loads on the feeder are taken into account.
Document “A review of impedance-based fault locating experience”; Edmund O. Schweitzer; 14th annual Iowa-Nebraska system protection seminar; Oct. 16, 1990; Omaha, Nebr., discloses a calculation procedure for locating a ground fault on a non-homogeneous line. This solution is also computationally burdensome and thus difficult to implement in a protective relay.